Financial markets allow participants to modify their exposure to the future values of financial quantities (such as the price of oil, or interest rates) for which they are concerned. For example, a producer of oil can reduce his exposure to the oil price at a future time by “selling oil forward.” The producer enters a forward agreement by which he commits to deliver a specified amount of oil at a future date in exchange for receiving a specified amount of money per barrel of oil. The amount of money is known as the “forward price” of oil at the time of the transaction for that future date. The producer can also purchase a put option with a strike of, for example, $20 for that date on that amount of oil. This put option gives the producer the rights to sell the amount of oil for $20 per barrel on that future date to the writer of the option. Alternatively, if the price per barrel ends up below $20, the producer could receive the difference between the price of oil per barrel and $20 for the amount of oil in question. As another example, a consumer of oil (such as an airline) could purchase, for example, a $30 strike call option on some amount of oil for a future date. This call option gives the consumer of oil the right to purchase that amount of oil at that date for $30 from the writer of the option.
The put and call options described above are simple examples of the general concept of “derivative securities” (or simply “derivatives,” sometimes also referred to as “options”). A derivative security is a cash flow (or a set of cash flows) that is derived from a set of financial market quantities in whatever way the counterparties engaging in trading that derivative agree upon.
Because the payoff of derivatives is in general not known until they expire (i.e., until all market quantities that the payoff depends upon have been determined), the current value of a position in a derivative is usually not evident. Therefore, in order for financial institutions to engage in such transactions, financial institutions use mathematical models to price derivatives (i.e., to determine their current value to the counterparties). The models used for this purpose differ widely in complexity and in the various details involved, but in general they usually attempt to assign risk neutral probabilities to the various payoffs possible, and from these probabilities derive the current value.
Information such as historical volatilities and correlations can be used for guidance in the design of the model (i.e., what kind of equations to use). Furthermore, a calibration process is usually used to ensure consistency of the actual model parameters with a set of option prices observable in the market and used as a reference.